Question

write the linear equation that gives the rule for this table.

x | y
5 | 2
6 | 3
7 | 4
8 | 5

write your answer as an equation with y first, followed by

Explanation:

Step1: Find the slope (m)

The formula for slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Using points (5, 2) and (6, 3):
\( m = \frac{3 - 2}{6 - 5} = \frac{1}{1} = 1 \)

Step2: Find the y-intercept (b)

Use the slope-intercept form \( y = mx + b \) and a point (e.g., (5, 2)):
\( 2 = 1(5) + b \)
\( 2 = 5 + b \)
\( b = 2 - 5 = -3 \)

Step3: Write the equation

Substitute \( m = 1 \) and \( b = -3 \) into \( y = mx + b \):
\( y = x - 3 \)

Answer:

\( y = x - 3 \)